Product rule for differentiation
Statement for two functions
If two (possibly equal) functions are differentiable at a given real number, then their pointwise product is also differentiable at that number and the derivative of the product is the sum of two terms: the derivative of the first function times the second function and the first function times the derivative of the second function.
Statement with symbols
Suppose and are functions, both of which are differentiable at a real number . Then, the product function , defined as is also differentiable at , and the derivative at is given as follows:
If we consider the general expressions rather than evaluation at a particular point , we can rewrite the above as: